On the group of homeomorphisms on R: A revisit

Kamaludheen Ali Akbar; T. Mubeena

doi:10.4995/agt.2022.16143

Authors

Kamaludheen Ali Akbar Central University of Kerala
T. Mubeena University of Calicut

DOI:

https://doi.org/10.4995/agt.2022.16143

Keywords:

Group of homeomorphisms, Normal subgroups, Dynamical systems, Fixed points, Conjugacy, bounded functions

Abstract

In this article, we prove that the group of all increasing homeomorphisms on R has exactly five normal subgroups, and the group of all homeomorphisms on R has exactly four normal subgroups. There are several results known about the group of homeomorphisms on R and about the group of increasing homeomorphisms on R ([2], [6], [7] and [8]), but beyond this there is virtually nothing in the literature concerning the topological structure in the aspects of topological dynamics. In this paper, we analyze this structure in some detail.

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Author Biographies

Kamaludheen Ali Akbar, Central University of Kerala

Department of Mathematics, School of Physical Sciences

T. Mubeena, University of Calicut

Department of Mathematics, School of Mathematics and Computational Science

References

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